One card is selected at random from a standard 52-card deck of playing cards. What is the probability that the card selected is not a spade?
In a standard 52-card deck, there are 4 Aces. We can figure out the probability of drawing a card that isn't a spade in two ways:
There are four 2s, four 3s,... all the way up to 4 Kings (12 ordinal cards in all, with each ordinal having four suits), and so we can say:
which works out to be
We can also do this by saying that there are 4 cards we don't want from a collection of 52, and so: